Mathematics, 30.03.2020 23:37 zay12350

The diameters of pencils produced by a certain machine are normally distributed with a mean of 0.30 and a standard deviation of 0.01. What is the probability that the diameter of a randomly slected pencil will be tween 0.21 and .29 inches

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Answer from: jrenwick001

The probability that the diameter of a randomly selected pencil will between 0.21 and 0.29 inches is 0.15865.

Step-by-step explanation:

We are given that the diameters of pencils produced by a certain machine are normally distributed with a mean of 0.30 and a standard deviation of 0.01.

Let X = diameters of pencils produced by a certain machine

SO, X ~ N( $\mu = 0.30,\sigma^{2} = 0.01^{2}$ )

The z-score probability distribution is given by ;

Z = $\frac{X-\mu}{\sigma}$ ~ N(0,1)

where, $\mu$ = mean diameter = 0.30

$\sigma$ = standard deviation = 0.01

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.

Now, the probability that the diameter of a randomly selected pencil will between 0.21 and 0.29 inches is given by = P(0.21 inches < X < 0.29 inches)

P(0.21 < X < 0.29) = P(X < 0.29) - P(X $\leq$ 0.21)

P(X < 0.29) = P( $\frac{X-\mu}{\sigma}$ < $\frac{0.29-0.30}{0.01}$ ) = P(Z < -1) = 1 - P(Z $\leq$ 1)

= 1 - 0.84134 = 0.15866

P(X $\leq$ 0.21) = P( $\frac{X-\mu}{\sigma}$ $\leq$ $\frac{0.21-0.30}{0.01}$ ) = P(Z $\leq$ -9) = 1 - P(Z < 9)

Now, for finding the P(Z < 9) in the z table we can observe that the maximum x value which the z table represent is 4.40 with an area of 0.99999. So, we can assume the P(Z < 9) to be 0.99999.

So, P(X $\leq$ 0.21) = 1 - P(Z < 9) = 1 - 0.99999 = 0.00001

Therefore, P(0.21 < X < 0.29) = 0.15866 - 0.00001 = 0.15865

Hence, probability that the diameter of a randomly selected pencil will between 0.21 and 0.29 inches is 0.15865.

Answer from: Quest

a)(x-2)^2+(y-1)^2=9

step-by-step explanation:

(picture explains)

Answer from: Quest

the correct answer is a) they believe they have a "just cause."

islamic terrorists justify their violent actions because they believe they have a "just cause."

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since the very beginning of the conflict with israel, islam is fighting a “sacred war”, respecting the words stated in the qur’an. they fight against the domination of the western countries and to defend their occupied territories.